related to https://math.stackexchange.com/q/2316201/453800?sgp=2
I redid it again trying to use commentars suggestion here and also the experience I got from trying to prove that Mills orbitspher is of type G.
I will probably publish a much nicer proof than you find in GUTCP perhaps tonight, well see. But the definitin and question has a much better form now. Hope that you
enjoy it and agree.
/Stefan
I assumed that for a point p in the sphere, there is a function F : p -> (f_1(p),...,f_k(p)). Hense the superscript k - that usually is the cardinality.
I assumed that there was a fixed number of imersions. This formulation can most probably be generalized. Later I say that for small enough
measurable sets A, dS 2(A) = \mu(f_1(A)) + ... + \mu(f_k(A)) i will probably need to do the example thoroughly in order to understand if this is
enough. Perhaps we need to make use of differential geometry. As I think THHuxley indicated.
Display MoreI tried to indicate an example which the Total is not equal to 0, I indicated the construction and it is included in Mills text. Shall I add page after page with a proper deduction? Can't I refer to his book?
The merit of what you are doing (unlike anything I've seen in Mills book) is that what you say (with some tweaking not yet complete) is precise and can be properly understood with no hand waving.
I need a similar description of Mills' claimed example - using maths not angular momentum and loops.
As far as hbar/2. hbar comes from the equations and this factor is simple, it could be no doubt adduced from many models classical, QM, right or wrong.
It is not rigor, but it's at least without angular momentum and clean, see the commentary in the question. My next step will be to try make that example in rigor and link to it, cause it will be too much to put in directly
THHuxleynew wrote:
> After all the hand-waving physical model you wish to hook to this question
The hand waving can be made rigid with a clear model and assumptions and lead to the correct ionization energy to 3 correct figures. This is not the difficult part.
The clear difficulty is to understand if hbar / 2 is special or just a tuning. Everything is precise. I think that this is a deep result and I feel that it has importance. I'm
sure that if QM is right this is a deep connection to understand the intrinsic spin, perhaps we can find similar systems that cater more to the QM.
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Anyone trying to follow this will need to reference the correctly formatted question:
https://math.stackexchange.com…uniform-geodesics#2316201
I have a problem with your question, which is that I don't understand how you define the mapping F:
Furthermore if we take F:S2←P(I×S1)F:S2←P(I×S1), P(⋅)P(⋅) the power set, as the mapping of a point of the sphere towards a discrete point of the geodesics covering that point, a function that we constrain G so that it exists.
F would appear to be a function domain I X S1 (the set of all points on all great circles) and range S2 (the surface of a sphere embedded in R3). I think you need the arrow in the opposite direction so that with F you are mapping a point on S2 to the set of all great circles that go through that point? I don't understand how this constrains G because it will exist (though may be trivial) for all G. I also expect that you actually require the existence of the Euclidean metric on R3 which induces a manifold on the embedded S2 - because you assume differential structure below.
The constraint on Mu is central to this definition:
Then we also constrain the measure μμ to satisfy ∀p∈S2 :(∑β∈F(p)dμ(β)=1/(4π)dS2∀p∈S2 :(∑β∈F(p)dμ(β)=1/(4π)dS2
Mu is defined to be a positive measure on I X S1. S1 is embedded in R2 and inherits a manifold structure from that embedding. I however is a set with no metric structure. That is OK, the fact that Mu is a measure will impose a measure (but not metric nor even topology) on I X S1. I think however you want this measure to be compatible with the implicit embedded local metric on S1? And maybe (see below) you want some extra structure on I.
Beta is the set of all great circles through p and is a subset of P(I X S1). Mu(beta) is therefore the measure on this subset. I think you are actually using the induced manifold structure of S2 here (p in S2) and saying in this constraint that the measure must be locally symmetric wrt any rotation of S2 (basically, small patches on S2 with the same area will have the same measure).
For this to be a proper question we need it to be expressed much more tightly. Also, I suspect that we don't need S1. The whole problem becomes simpler to think about if you just ask questions about the nalpha. For example the set of nalpha corresponding to great circles going through a point p is makes the great circle whose normal is itself p. A pleasing and well-known symmetry.
Now I'm still unclear about the symmetry here induced on G. The obvious symmetry satisfying this condition leads to Total = 0. It would help elucidate this to show constructively (without introducing concepts from physics like angular momentum) the existence of any non-trivial solution with Total not equal to 0. You just need to give the solution as math and show it complies.
When you have tied this up I still doubt your result is true, unless you have the full euclidean induced manifold structure on S2 and something similar on I. After all the hand-waving physical model you wish to hook to this question certainly has I isomorphic to S2 and a natural euclidean metric (that is - the set of great circles on S2 is isomorphic to their normals, which are isomorphic to S2. In fact this isomorphism makes a duality). I also expect (but don't know) that it can be shown true much more trivially with a much simpler isomorphic structure than you have set up here. I'm uneasy about mixing a measure with a manifold which seems plain weird.
You can't ask people to think about this without some more work on what this constraints really means. This, together with the above loose points in the definition, make for the bad rating I believe.
I think that we can't skip the loops because you need to map points on several loops to a point on the sphere.
phew another version is finished, still very abstract but more concrete then before and it should be well defined. Next it would be nice to show Mills example in rigid mathematics, with lot's of steps.
CU
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Anyone trying to follow this will need to reference the correctly formatted question:
https://math.stackexchange.com…uniform-geodesics#2316201
I have a problem with your question, which is that I don't understand how you define the mapping F:
Furthermore if we take F:S2←P(I×S1)F:S2←P(I×S1), P(⋅)P(⋅) the power set, as the mapping of a point of the sphere towards a discrete point of the geodesics covering that point, a function that we constrain G so that it exists.
F would appear to be a function domain I X S1 (the set of all points on all great circles) and range S2 (the surface of a sphere embedded in R3). I think you need the arrow in the opposite direction so that with F you are mapping a point on S2 to the set of all great circles that go through that point? I don't understand how this constrains G because it will exist (though may be trivial) for all G. I also expect that you actually require the existence of the Euclidean metric on R3 which induces a manifold on the embedded S2 - because you assume differential structure below.
The constraint on Mu is central to this definition:
Then we also constrain the measure μμ to satisfy ∀p∈S2 :(∑β∈F(p)dμ(β)=1/(4π)dS2∀p∈S2 :(∑β∈F(p)dμ(β)=1/(4π)dS2
Mu is defined to be a positive measure on I X S1. S1 is embedded in R2 and inherits a manifold structure from that embedding. I however is a set with no metric structure. That is OK, the fact that Mu is a measure will impose a measure (but not metric nor even topology) on I X S1. I think however you want this measure to be compatible with the implicit embedded local metric on S1? And maybe (see below) you want some extra structure on I.
Beta is the set of all great circles through p and is a subset of P(I X S1). Mu(beta) is therefore the measure on this subset. I think you are actually using the induced manifold structure of S2 here (p in S2) and saying in this constraint that the measure must be locally symmetric wrt any rotation of S2 (basically, small patches on S2 with the same area will have the same measure).
For this to be a proper question we need it to be expressed much more tightly. Also, I suspect that we don't need S1. The whole problem becomes simpler to think about if you just ask questions about the nalpha. For example the set of nalpha corresponding to great circles going through a point p is makes the great circle whose normal is itself p. A pleasing and well-known symmetry.
Now I'm still unclear about the symmetry here induced on G. The obvious symmetry satisfying this condition leads to Total = 0. It would help elucidate this to show constructively (without introducing concepts from physics like angular momentum) the existence of any non-trivial solution with Total not equal to 0. You just need to give the solution as math and show it complies.
When you have tied this up I still doubt your result is true, unless you have the full euclidean induced manifold structure on S2 and something similar on I. After all the hand-waving physical model you wish to hook to this question certainly has I isomorphic to S2 and a natural euclidean metric (that is - the set of great circles on S2 is isomorphic to their normals, which are isomorphic to S2. In fact this isomorphism makes a duality). I also expect (but don't know) that it can be shown true much more trivially with a much simpler isomorphic structure than you have set up here. I'm uneasy about mixing a measure with a manifold which seems plain weird.
You can't ask people to think about this without some more work on what this constraints really means. This, together with the above loose points in the definition, make for the bad rating I believe.
Thanks, this is good feedback.
So what I'm struggling to say rigorously is:
We consider a subset of all geodesics and specifically a subset where only a discrete number of selected geodesics goes through a point p on the sphere, so for a point, there is a selection of geodesics, {S_a_1,S_a_2,...} and for each of the geodesics you have a point which cover p, e.g. you have pairs {(a_1,p_1),(a_2,p_2),...} eg a subset of (I x S^1) e.g. en element of the powerset now each of these points has a measures or if you like infinetismal weights mu(a_1,p_1), mu(a_2,p_2),... and they should sum up to 1/4pi dS. and then you can integrate the surface and recover total mass of 1. So this is a fancy way of saying that the sum of the coverings is uniform. In order for there to be a covering of type G I assume that this mapping F should exists and it does in Mills example (but it is hidden). Your good point is that perhaps I must better motivate the existance of F.
> Mu is defined to be a positive measure on I X S1. S1 is embedded in R2 and inherits a manifold structure from that embedding. I however is a set with no metric structure. That is OK, the fact that Mu is a measure will impose a measure (but not
> metric nor even topology) on I X S1. I think however you want this measure to be compatible with the implicit embedded local metric on S1? And maybe (see below) you want some extra structure on I.
I am sloppy or rusty whatever you like to call it and do find it tricky to get the formulation right, I understand your points here.
> Beta is the set of all great circles through p and is a subset of P(I X S1). Mu(beta) is therefore the measure on this subset. I think you are actually using the induced manifold structure of S2 here (p in S2) and saying in this constraint that the measure > must be locally symmetric wrt any rotation of S2 (basically, small patches on S2 with the same area will have the same measure).
Yes
> For this to be a proper question we need it to be expressed much more tightly. Also, I suspect that we don't need S1. The whole problem becomes simpler to think about if you just ask questions about the nalpha. For example the set of
> nalpha corresponding to great circles going through a point p is makes the great circle whose normal is itself p. A pleasing and well-known symmetry.
> Now I'm still unclear about the symmetry here induced on G. The obvious symmetry satisfying this condition leads to Total = 0. It would help elucidate this to show constructively (without introducing concepts from physics like angular momentum)
> the existence of any non-trivial solution with Total not equal to 0. You just need to give the solution as math and show it complies.
I tried to indicate an example which the Total is not equal to 0, I indicated the construction and it is included in Mills text. Shall I add page after page with a proper deduction? Can't I refer to his book?
> When you have tied this up I still doubt your result is true, unless you have the full euclidean induced manifold structure on S2 and something similar on I. After all the hand-waving physical model you wish to hook to this question certainly has I
> isomorphic to S2 and a natural euclidean metric (that is - the set of great circles on S2 is isomorphic to their normals, which are isomorphic to S2. In fact this isomorphism makes a duality). I also expect (but don't know) that it can be shown true
> much more trivially with a much simpler isomorphic structure than you have set up here. I'm uneasy about mixing a measure with a manifold which seems plain weird.
The generality of measures is perhaps too much, perhaps I should be working with manifolds as you say.
What about this. We want that for all measurable set A on S^2, we have a set F(A) \in P(I x S^1) so that F(A) is measurable with mu and mu(F(A)) = n(A), n being the
uniform measure on S^2?
I agree that you wouldn't necessarily describe the problem in the same way for a professor you're taking the question to. But you can have more than one formulation of the problem: one for Mathematics Stack Exchange which is concise (even more concise than what I have above), and another one that is for the people you know that you're going to talk to. You can have both descriptions at once, because there are many electrons and many pixels in the world.
Would you like to nuke the example? Would you like to nuke the summary? Mathematicians like to put section things as Theorems and Definitions and I like that too. I think that we should keep that tradition.
Stefan, how about this further editing of your question?
See how it is very short? Is there any way you can make it even shorter?
I can leave out details and it results in the executive summary. So that is the short version. But I want to make a fully mathematical definition as well and get it correct on a Phd level
then you get the quote above. I could leave it out but I'm planning to engage professors in this, and then this definition is a bonus point in their eyes. _Making things well defined
mathematically lead to a few more details than the summary, which is fine for a person to grasp what it is all about.
Okey. I severely redrafted the question at stack exchange.
A compact executive summary and a very mathematical and clean formulation. Then I added the commentary to my blog
http://www.c-lambda.se/a-deep-question.html, you may comment there if you like or here as well.
I did a rewrite of the stack exchange question and are on -1 now, one up from -2. I found some bugs and tried to make things clearer e.g. more well defined. Also
I clearly separated the commentary from the question so that the question is clearly stated. Now only ignorant trolls would downvote it. E.g. people with little
knowledge of math but a diss-like for Mills, we should be clear that those will try to downvote this question now if they can which is downright stupid.
Anyway the outcome is not important and if it is not upvoted it shows that stackexchnge is flawed. I can simply ask people at my old institution.
First, I'm not an academic.
The earlier challenge that we were discussing was not to disprove anything of Mills's. It was a challenge to make Mills's implicit exposition of the neutron-electron mass ratio in GUT-CP explicit, by filling in the missing steps in which the various equations are combined and derived from one another. My suspicion is that the gaps cannot be filled, because the equations just thrown in there to look impressive, and the final result, the equation for the neutron-electron mass ratio, is not really related to all of that fancy-sounding exposition. In the earlier thread I was hoping that someone who disagreed with this impression of mine and had the energy to fill in the gaps would be willing to do so.
Regarding your StackExchange question — I was hoping you would edit and reword it so that someone would answer it and it would get some upvotes.
Yes I can reword it, so it feel less clumsy in the mouth, e.g. easier to grasp as a reader. But you are asking to condense it and I simply fail to see what I can do about that and they actually downvoted me when I left out parts of the definition.
If you like we can continue the old discussion. As you now this part is not as clear as one would hope and I pointed out a few weaknesses as we did go. The thing is that the part where we hung up was not a point where we should hung. I think that the issues might be elsewhere. Anyway if you like I could tex out the steps in solving that equation for you and we could take up the discussion again. But later. I think that what I'm (we) are doing now is more important.
I will ask my fellows at my old math institution about the stack exchange question. I can always come back with additional info if you are interested or ask them to comment on the question at stack exchange.
Display MoreEric Walker wrote "his task is even bigger"
weak .. strong interactions.. Mills has his eye on the stars , I think that's where his end task is.
His fifth force generator is postulated to go through the Earth's atmosphere in a matter of seconds..
Velocity 9 km/s for a 1000 tonne vehicle at 200 amps (of pseudoelectrons.) and 47 million Volts..
Without a wobble... that's some American dream!
That would of cause be awsome if true, but it's a loooooong way for it to be true. Meanwhile we will argue till our fingers bleed about microcosmosology. I kind like to point out to my friends how much star trek
Mills ideas are. I always say that it is a nice fantasy, and fun to watch but with the added tenseness that maybe maybe it's all true.
You've made a claim that I failed to acknowledge a simple solution. Shall we reprise that discussion and see if your claim has merit, or, alternatively, whether you simply failed to fill out some details and allowing your argument to be vague and hand-wavy (the opposite of an explicit exposition)?
No I think that you should be a good akademic and prove that the solution to the equation is wrong, I did my duty as a good critical akademic when it comes to pointing out weaknesses of Mills deduction en the stack exchange question. It's only right that you play that role this time.
Display MoreYou provided one interpretation, namely this one. I provided another possible interpretation. Perhaps yours is the correct one.
One of my two bachelor's degrees was in mathematics. The only thing that could be concluded from the earlier discussion is that you are not accustomed to the rigors of setting out a mathematical proof and the demands that are raised in this connection. I deduce therefore that you did not get a degree in mathematics.
The mathematics StackExchange site is no doubt a site run by brilliant mathematicians who can help you out with your question. The decisions that you make will affect whether you get a question answered there. The choice is yours.
This is a case of information conflicting each other. You failed, in our previous discussion, to acknowledge that a quite simple equation has a solution, If you just said that it had the solution shown, but wanted more steps for others to see I have bought that. The thing is, that the solution of that equation was so standard that normally in research discussions, the middle steps is left out. So I deduced that your skill was not that good and lost interest. But in either case, what should I leave out of the definition of the system of type G? give me some clear direction! I can't find anything that is not needed for stringence or to explain a mathematical concept for the more ignorant. Shall I leave out the comment that geodesics are great circles, is that what you mean with making it more compact? Well I'm actually think that you are right about the staff, but the thing it was downvoted to -2 quickly before the quality of it went up and I think that it is due to this reason not seen by the good ones. Only people who can't upvote.
Display MoreI have 90 viewres and the last 70 of them did at least not dwonvote or couldn't upvote.
Looks understandable to me.
You don't have all your hens at home.
Suck it and see.
If no response in a week. Reformat and post again.
Forums in theses days of short attention spans are unpredictable.
lol, I do some misstakes in english sometimes or misses a point, just sloppiness and and effect of putting the cheek out, probably not a hen issue.
You are talking about what should be true. I am talking about is true, right now. Do you want to get your question answered? If so, you should make it more compact and conceal the allusions to Mills's theory. Or maybe I'm wrong, and your analysis that it was simply because you needed to provide more detail is correct. I have already mentioned another possibility for why the question hasn't been further downvoted: that people see that it is already at -2 points, and they might feel sorry for you since you seem sincere. Perhaps I'm incorrect in thinking this might be the case.
Don't you listen to what I'm saying. It was much more compact before and it was then I got the down voting, the voters wanted me to be more stringent. I'm sorry to say but you are not a matematician and weak at it. That's clear from our previous discussion
So I don't take your advice on this matter due to this. When it comes to me I can point to a piece of masterwork I did around in the 90-ies:
http://www.sciencedirect.com/s…cle/pii/S0304414900001009
Actually if the site is run by morons and they refuse to upvote it it's not my buisness. Then I know that they are a bunch of clowns or that there is a conspiarcy or such. I don't care I've done whats objectively demanded of me as a good citizen. But I will of cause skip this path and have a chat with my former superviser and see if they can find some information.
I would put it differently. It is hard to follow several volumes of word salad, because the individual details are disjoint and do not provide an actual mathematical argument.
well I say vague meaning that there are things I can't follow to be polite. But i do recognize that some stuff he claim seams to be correct, but his deduction is over complicated and wrong. But still he can be correct.
A faulty proof of a theorem does not prove that the theorem is wrong, just that we don't know and a proof of it's incorrectness is needed to conclude. This is in essens the vagness and although Mills sometimes put up a bad proof,
people on the other side put up bad counter proof. As an example it is not acknowledged that Mills charge distribution lead to a non radiating conition but it is commonly said whithout a correct proof that he is wrong
that they do indeed radiate. Mills have two proofs of it and one of them is wrong. I did my own proof of it and it is clear that those distributions indeed does not radiate and also have all the potential needed to produce
a system we call atoms. I would actually say that I believe both sides on this story are fringe. I have gotten a lot of laughs ploughing through bad and faulty arguments. This is fringe yes, but I do enjoy it and sometimes
from fringness items of pure gold can be found, The stack exchange question is a good example of that.
The quesr
Perhaps I should reverse this question and ask whether you're crazy? No, I'm not crazy. Mills is fringe. You should accept this fact right now, before going to a StackExchange site again and predictably getting your question downvoted. The mathematics may not be fringe, but your interest in the mathematics is connected to someone who is fringe, and many people will lose interest at this point who could have otherwise provided useful commentary on the mathematics. Here we're talking about the most effective strategy in getting your question addressed, and not the question itself. It is ineffective to bring in a disreputable source.
Whether someone is fringe is only indirectly related to whether they're correct. In this case, it seems that Mills is both fringe and incorrect in suggesting that his system can supplant quantum mechanics
I gave all the information that anyone objective and good at math can see the value of it, see that it is a well defined problem, a problem that an expert would love to answer, is fun and entertaining, is challanging and has a depth. The downvoting was because I left out details and they couldn't see if the setup was well defined or not. That Mills is challanging QM is not an issue here, and even for a physists he must admit that it is a cool and interesting coincidence that such a natural and physical well balanced model indeed give the correct figures. The thing is that Mills could still be wrong in large and QM can still be right, but this isolated fact seam to have physical weight in some way and should be a known fact to the community. All else is fringe and the opposite of knowledge and good akademic behavior.
The weak interaction is quite invisible to the electromagnetic interaction, and vise versa. The electron and the proton participate in electron capture because the electron is a lepton. No electrical fields are involved. (So far as we know.)
The weak interaction does not work over long distances. Its range is 0.1 percent of the diameter of a proton. The electron orbital must overlap with the proton for the weak interaction to operate.
The dirac fields couples with electromagnets, I think you need to give me some background on why you don't think that a resonant coupling can't ork. What I mean with this is just as with resonant couplings you see nada when there is no resonanse e.g. it is only for special setups of the EM fields that you will get a measurable effect so it is quite possible that we missed it. Allso Mills model is an attractive idea due to it's simplicity, everything is electromagnetic theory and also the weak forces and strong forces are actually a special electromagnetic phenomena. Not a normal one usually thugh, there are some extream extensions done to Maxwells equations e.g. generalizing it to source termns that are distributions e.g. a generalisation of functions.
